The weights \(\rho _n^{(j)}\)  are quite important. On one hand, the convex hull formed by the \(W(\mathfrak {k}, \mathfrak {t}_f)\)  orbits of the weights \(2\rho _n^{(j)}\) , \(0\le j\le 62\) , is called the unitarily small (u-small for short henceforth) convex hull by Salamanca-Riba and Vogan [1]}. A \(K\) -type (or \(\mathfrak {k}\) -type) is called u-small if its highest weight lies in this polyhedron. Otherwise, we will say it is u-large.
